Stress analysis of transversely loaded functionally graded plates with a higher order shear and normal deformation theory

Abstract

Static analysis of orthotropic functionally graded elastic, rectangular, and simply supported (diaphragm) plates under transverse loads is presented based on a higher order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson's ratios of the FG plates are assumed to be constant, but their Young's modulii vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modelled as an exponential function. The governing equations of equilibrium for the FG plates are derived on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. Several examples of isotropic, orthotropic and FG plates are presented. The accuracy of the numerical solutions has been compared with the solutions obtained by other models and the exact three dimensional (3D) elasticity solutions.